#riemann-geometry

Continuing on previous posts on affine connection, In this posting we will cover why we called above connection as affine connection. First review, affine connection satisfies In a coordinate basis, affine

In this posting, we will derive some transformation law of connection. Thus see that this connection is not tensor but its anti-symmetrized transforms as a tensor. In this posting, we will not directly

In the last posting, we derive some equations. Using these results as an exercise let's compute the equation of motion of low-energy effective action of string theory. The equations of motion are following

In my previous posts, I have been writing posts about Riemann geometry. Today I want to talk about variation in Riemannian geometry and further take one exercise, obtaining equation of motion of Low-energy

In my previous posting on Riemann geometry [math,computation] Riemann geometry: Ricci scalar written in metric explicitly we express Ricci scalar in terms of metric only. In this post we will express Ricci

This is a English version of my former post The purpose of this posting is to express Ricci scalar in terms of metric only. i.e., derive Convention Define Covariant derivative as follows Under this convention